As already mentioned in secExample3, since the problem has a large global Péclet number, namely \(\mathbf {Pe}_g = \mathfrak {a} = 10^4\) , approximate solutions belonging to piecewise polynomial spaces exhibit spurious oscillations until the discretization is fine enough to resolve the sharp layers featured by the exact solution.
To overcome this issue, it is common to rely on stabilization methods such as the SUPG and GLS method; see [1]}, [2]}. Typically, stabilization methods remove spurious oscillations but at the same time “smooth out” the layers featured by the exact solution. Their efficiency deeply depends on a careful choice of some parameters appearing in the various stabilization methods.
